Optimal error estimates for Nedelec edge elements for time-harmonic Maxwell's equations

Liuqiang Zhong, Shi Shu, Gabriel Wittum, Jinchao Xu

Research output: Contribution to journalArticle

26 Scopus citations

Abstract

In this paper, we obtain optimal error estimates in both L2-norm and H(curl)-norm for the Nedelec edge finite element approximation of the time-harmonic Maxwell's equations on a general Lipschitz domain discretized on quasi-uniform meshes. One key to our proof is to transform the L2 error estimates into the L2 estimate of a discrete divergence-free function which belongs to the edge finite element spaces, and then use the approximation of the discrete divergence-free function by the continuous divergence-free function and a duality argument for the continuous divergence-free function. For Nédélec's second type elements, we present an optimal convergence estimate which improves the best results available in the literature.

Original languageEnglish (US)
Pages (from-to)563-572
Number of pages10
JournalJournal of Computational Mathematics
Volume27
Issue number5
DOIs
StatePublished - Sep 1 2009

All Science Journal Classification (ASJC) codes

  • Computational Mathematics

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